In this paper Chaos Collocation method coupled to Fictitious Domain approach has been applied to one-
and two-dimensional elliptic problems defined on random domains in order to demonstrate the accuracy
and convergence of the methodology. Chaos Collocation method replaces a stochastic process with a set
of deterministic problems, which can be separately solved, so that the big advantage of Chaos Collocation
is that it is non-intrusive and existing deterministic solvers can be used. For the analysis of differential
problems obtained by Chaos Collocation, Fictitious Domain method with Least-Squares Spectral Element
approximation has been employed. This algorithm exploits a fictitious computational domain, where the
boundary constraints, immersed in the new simple shaped domain, are enforced by means of Lagrange
multipliers. For this reason its main advantage lies in the fact that only a Cartesian mesh, that represents
the enclosure, needs to be generated. Excellent accuracy properties of developed method are
demonstrated by numerical experiments.
